Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(1057,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.1057");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.t (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1333.23 | ||
Character | \(\chi\) | \(=\) | 1380.1333 |
Dual form | 1380.2.t.a.1057.23 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.72321 | + | 1.42497i | −0.770644 | + | 0.637265i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.66865 | − | 1.66865i | −0.630690 | − | 0.630690i | 0.317552 | − | 0.948241i | \(-0.397139\pi\) |
−0.948241 | + | 0.317552i | \(0.897139\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.0251310i | − | 0.00757729i | −0.999993 | − | 0.00378865i | \(-0.998794\pi\) | ||
0.999993 | − | 0.00378865i | \(-0.00120597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.31706 | + | 4.31706i | 1.19734 | + | 1.19734i | 0.974961 | + | 0.222375i | \(0.0713810\pi\) |
0.222375 | + | 0.974961i | \(0.428619\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.22610 | − | 0.210891i | −0.574777 | − | 0.0544518i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.93368 | + | 2.93368i | 0.711521 | + | 0.711521i | 0.966853 | − | 0.255333i | \(-0.0821849\pi\) |
−0.255333 | + | 0.966853i | \(0.582185\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.73401 | −1.31547 | −0.657736 | − | 0.753249i | \(-0.728486\pi\) | ||||
−0.657736 | + | 0.753249i | \(0.728486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.35982i | − | 0.514956i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.66047 | − | 4.49920i | −0.346232 | − | 0.938149i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.938928 | − | 4.91105i | 0.187786 | − | 0.982210i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.21783i | 1.34032i | 0.742218 | + | 0.670158i | \(0.233774\pi\) | ||||
−0.742218 | + | 0.670158i | \(0.766226\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.64554 | −1.55278 | −0.776392 | − | 0.630250i | \(-0.782952\pi\) | ||||
−0.776392 | + | 0.630250i | \(0.782952\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0177703 | − | 0.0177703i | 0.00309342 | − | 0.00309342i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.25321 | + | 0.497665i | 0.887954 | + | 0.0841208i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.47729 | − | 6.47729i | −1.06486 | − | 1.06486i | −0.997745 | − | 0.0671152i | \(-0.978620\pi\) |
−0.0671152 | − | 0.997745i | \(-0.521380\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.10524i | 0.977621i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0620681 | −0.00969341 | −0.00484671 | − | 0.999988i | \(-0.501543\pi\) | ||||
−0.00484671 | + | 0.999988i | \(0.501543\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.43676 | + | 5.43676i | −0.829097 | + | 0.829097i | −0.987392 | − | 0.158295i | \(-0.949400\pi\) |
0.158295 | + | 0.987392i | \(0.449400\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.42497 | − | 1.72321i | −0.212422 | − | 0.256881i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.36786 | + | 4.36786i | −0.637117 | + | 0.637117i | −0.949843 | − | 0.312726i | \(-0.898758\pi\) |
0.312726 | + | 0.949843i | \(0.398758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.43123i | − | 0.204461i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.14884i | 0.580954i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.27165 | + | 9.27165i | −1.27356 | + | 1.27356i | −0.329352 | + | 0.944207i | \(0.606830\pi\) |
−0.944207 | + | 0.329352i | \(0.893170\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0358109 | + | 0.0433061i | 0.00482875 | + | 0.00583940i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.05455 | − | 4.05455i | −0.537039 | − | 0.537039i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.10077i | 0.273497i | 0.990606 | + | 0.136748i | \(0.0436652\pi\) | ||||
−0.990606 | + | 0.136748i | \(0.956335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.81366i | 0.616327i | 0.951333 | + | 0.308163i | \(0.0997143\pi\) | ||||
−0.951333 | + | 0.308163i | \(0.900286\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.66865 | − | 1.66865i | 0.210230 | − | 0.210230i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.5909 | − | 1.28754i | −1.68574 | − | 0.159700i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.147877 | + | 0.147877i | 0.0180661 | + | 0.0180661i | 0.716082 | − | 0.698016i | \(-0.245934\pi\) |
−0.698016 | + | 0.716082i | \(0.745934\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00729 | − | 4.35555i | 0.241649 | − | 0.524346i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.45924 | −0.529215 | −0.264607 | − | 0.964356i | \(-0.585242\pi\) | ||||
−0.264607 | + | 0.964356i | \(0.585242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.58272 | − | 1.58272i | −0.185243 | − | 0.185243i | 0.608393 | − | 0.793636i | \(-0.291814\pi\) |
−0.793636 | + | 0.608393i | \(0.791814\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.13656 | − | 2.80871i | 0.477649 | − | 0.324322i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0419348 | + | 0.0419348i | −0.00477892 | + | 0.00477892i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.73841 | 0.645621 | 0.322811 | − | 0.946464i | \(-0.395372\pi\) | ||||
0.322811 | + | 0.946464i | \(0.395372\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.182671 | − | 0.182671i | 0.0200507 | − | 0.0200507i | −0.697010 | − | 0.717061i | \(-0.745487\pi\) |
0.717061 | + | 0.697010i | \(0.245487\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.23574 | − | 0.874953i | −1.00176 | − | 0.0949019i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.10377 | + | 5.10377i | −0.547182 | + | 0.547182i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.2895 | 1.09069 | 0.545343 | − | 0.838213i | \(-0.316399\pi\) | ||||
0.545343 | + | 0.838213i | \(0.316399\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 14.4073i | − | 1.51029i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.11332 | − | 6.11332i | −0.633922 | − | 0.633922i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.88091 | − | 8.17078i | 1.01376 | − | 0.838304i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8876 | − | 12.8876i | −1.30854 | − | 1.30854i | −0.922470 | − | 0.386069i | \(-0.873833\pi\) |
−0.386069 | − | 0.922470i | \(-0.626167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0251310 | 0.00252576 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.7220 | 1.56440 | 0.782201 | − | 0.623026i | \(-0.214097\pi\) | ||||
0.782201 | + | 0.623026i | \(0.214097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.79500 | + | 2.79500i | −0.275399 | + | 0.275399i | −0.831269 | − | 0.555870i | \(-0.812385\pi\) |
0.555870 | + | 0.831269i | \(0.312385\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.36268 | + | 4.06648i | 0.328164 | + | 0.396848i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.00287023 | + | 0.00287023i | 0.000277476 | + | 0.000277476i | 0.707246 | − | 0.706968i | \(-0.249938\pi\) |
−0.706968 | + | 0.707246i | \(0.749938\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.83662 | −0.463264 | −0.231632 | − | 0.972803i | \(-0.574407\pi\) | ||||
−0.231632 | + | 0.972803i | \(0.574407\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 9.16028i | − | 0.869455i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.78998 | − | 3.78998i | 0.356531 | − | 0.356531i | −0.506002 | − | 0.862533i | \(-0.668877\pi\) |
0.862533 | + | 0.506002i | \(0.168877\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.27257 | + | 5.38697i | 0.864671 | + | 0.502338i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.31706 | + | 4.31706i | −0.399112 | + | 0.399112i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.79054i | − | 0.897497i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9994 | 0.999943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0438888 | − | 0.0438888i | −0.00395732 | − | 0.00395732i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.38012 | + | 9.80073i | 0.481213 | + | 0.876604i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.03114 | + | 5.03114i | −0.446442 | + | 0.446442i | −0.894170 | − | 0.447728i | \(-0.852233\pi\) |
0.447728 | + | 0.894170i | \(0.352233\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.68873 | −0.676955 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.17258 | −0.102449 | −0.0512245 | − | 0.998687i | \(-0.516312\pi\) | ||||
−0.0512245 | + | 0.998687i | \(0.516312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.56803 | + | 9.56803i | 0.829654 | + | 0.829654i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.210891 | − | 2.22610i | 0.0181506 | − | 0.191592i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.1030 | + | 16.1030i | 1.37578 | + | 1.37578i | 0.851627 | + | 0.524149i | \(0.175616\pi\) |
0.524149 | + | 0.851627i | \(0.324384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.7001i | 1.58612i | 0.609145 | + | 0.793059i | \(0.291513\pi\) | ||||
−0.609145 | + | 0.793059i | \(0.708487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.17708 | −0.520204 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.108492 | − | 0.108492i | 0.00907257 | − | 0.00907257i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.2852 | − | 12.4379i | −0.854137 | − | 1.03291i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.01203 | − | 1.01203i | 0.0834710 | − | 0.0834710i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.92087 | −0.321210 | −0.160605 | − | 0.987019i | \(-0.551344\pi\) | ||||
−0.160605 | + | 0.987019i | \(0.551344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.38226 | 0.519381 | 0.259691 | − | 0.965692i | \(-0.416379\pi\) | ||||
0.259691 | + | 0.965692i | \(0.416379\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.93368 | + | 2.93368i | −0.237174 | + | 0.237174i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.8981 | − | 12.3196i | 1.19664 | − | 0.989536i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0603 | + | 10.0603i | 0.802901 | + | 0.802901i | 0.983548 | − | 0.180647i | \(-0.0578191\pi\) |
−0.180647 | + | 0.983548i | \(0.557819\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.1121 | −1.03986 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.73685 | + | 10.2783i | −0.373316 | + | 0.810045i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5575 | − | 15.5575i | −1.21856 | − | 1.21856i | −0.968137 | − | 0.250423i | \(-0.919430\pi\) |
−0.250423 | − | 0.968137i | \(-0.580570\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.00529990 | + | 0.0559442i | −0.000412597 | + | 0.00435525i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.5827 | − | 12.5827i | 0.973682 | − | 0.973682i | −0.0259809 | − | 0.999662i | \(-0.508271\pi\) |
0.999662 | + | 0.0259809i | \(0.00827092\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.2740i | 1.86723i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.73401i | − | 0.438490i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.47575 | − | 5.47575i | −0.416314 | − | 0.416314i | 0.467617 | − | 0.883931i | \(-0.345113\pi\) |
−0.883931 | + | 0.467617i | \(0.845113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.76155 | + | 6.62807i | −0.737904 | + | 0.501035i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.48547 | + | 1.48547i | −0.111655 | + | 0.111655i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.39989i | 0.403607i | 0.979426 | + | 0.201804i | \(0.0646802\pi\) | ||||
−0.979426 | + | 0.201804i | \(0.935320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.85131i | − | 0.286266i | −0.989703 | − | 0.143133i | \(-0.954282\pi\) | ||
0.989703 | − | 0.143133i | \(-0.0457176\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.40377 | + | 3.40377i | −0.251614 | + | 0.251614i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.3917 | + | 1.93182i | 1.49923 | + | 0.142030i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0737263 | − | 0.0737263i | 0.00539140 | − | 0.00539140i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.35982 | 0.171652 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.52181i | 0.182472i | 0.995829 | + | 0.0912360i | \(0.0290818\pi\) | ||||
−0.995829 | + | 0.0912360i | \(0.970918\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4431 | − | 16.4431i | −1.18360 | − | 1.18360i | −0.978804 | − | 0.204799i | \(-0.934346\pi\) |
−0.204799 | − | 0.978804i | \(-0.565654\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.69978 | − | 10.5206i | −0.623004 | − | 0.753398i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0590 | + | 11.0590i | −0.787924 | + | 0.787924i | −0.981154 | − | 0.193230i | \(-0.938104\pi\) |
0.193230 | + | 0.981154i | \(0.438104\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5439 | 0.889216 | 0.444608 | − | 0.895725i | \(-0.353343\pi\) | ||||
0.444608 | + | 0.895725i | \(0.353343\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.209130i | 0.0147509i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0440 | − | 12.0440i | 0.845324 | − | 0.845324i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.106957 | − | 0.0884451i | 0.00747017 | − | 0.00617728i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.49920 | − | 1.66047i | 0.312716 | − | 0.115411i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.144101i | 0.00996771i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.92577 | 0.614475 | 0.307238 | − | 0.951633i | \(-0.400595\pi\) | ||||
0.307238 | + | 0.951633i | \(0.400595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.15316 | − | 3.15316i | −0.216051 | − | 0.216051i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.62148 | − | 17.1159i | 0.110584 | − | 1.16729i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.4264 | + | 14.4264i | 0.979325 | + | 0.979325i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 2.23830i | − | 0.151250i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.3297i | 1.70386i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.09635 | − | 8.09635i | −0.542172 | − | 0.542172i | 0.381993 | − | 0.924165i | \(-0.375238\pi\) |
−0.924165 | + | 0.381993i | \(0.875238\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.91105 | + | 0.938928i | 0.327403 | + | 0.0625952i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.1918 | + | 19.1918i | 1.27380 | + | 1.27380i | 0.944077 | + | 0.329724i | \(0.106956\pi\) |
0.329724 | + | 0.944077i | \(0.393044\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.7187 | 1.17088 | 0.585442 | − | 0.810714i | \(-0.300921\pi\) | ||||
0.585442 | + | 0.810714i | \(0.300921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0593048 | −0.00390197 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.12902 | − | 2.12902i | −0.139477 | − | 0.139477i | 0.633921 | − | 0.773398i | \(-0.281444\pi\) |
−0.773398 | + | 0.633921i | \(0.781444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.30269 | − | 13.7508i | 0.0849781 | − | 0.897004i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.05767 | + | 4.05767i | 0.263574 | + | 0.263574i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.5239i | 1.58632i | 0.609013 | + | 0.793161i | \(0.291566\pi\) | ||||
−0.609013 | + | 0.793161i | \(0.708434\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.6804i | 1.20331i | 0.798757 | + | 0.601654i | \(0.205491\pi\) | ||||
−0.798757 | + | 0.601654i | \(0.794509\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.03946 | + | 2.46632i | 0.130296 | + | 0.157567i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.7540 | − | 24.7540i | −1.57506 | − | 1.57506i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.258336 | 0.0163714 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.61887i | − | 0.165302i | −0.996579 | − | 0.0826509i | \(-0.973661\pi\) | ||
0.996579 | − | 0.0826509i | \(-0.0263386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.113070 | + | 0.0417293i | −0.00710863 | + | 0.00262350i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.91197 | − | 7.14934i | −0.370222 | − | 0.447709i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.9282 | − | 20.9282i | 1.30546 | − | 1.30546i | 0.380811 | − | 0.924653i | \(-0.375645\pi\) |
0.924653 | − | 0.380811i | \(-0.124355\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.6166i | 1.34319i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.21783 | −0.446772 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.24246 | + | 5.24246i | −0.323264 | + | 0.323264i | −0.850018 | − | 0.526754i | \(-0.823409\pi\) |
0.526754 | + | 0.850018i | \(0.323409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.76522 | − | 29.1888i | 0.169866 | − | 1.79306i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.27579 | + | 7.27579i | 0.445271 | + | 0.445271i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 16.4697i | − | 1.00418i | −0.864816 | − | 0.502088i | \(-0.832565\pi\) | ||
0.864816 | − | 0.502088i | \(-0.167435\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.7600 | −1.01810 | −0.509049 | − | 0.860738i | \(-0.670003\pi\) | ||||
−0.509049 | + | 0.860738i | \(0.670003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.1875 | − | 10.1875i | 0.616575 | − | 0.616575i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.123420 | − | 0.0235962i | −0.00744249 | − | 0.00142291i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8812 | + | 14.8812i | −0.894125 | + | 0.894125i | −0.994908 | − | 0.100784i | \(-0.967865\pi\) |
0.100784 | + | 0.994908i | \(0.467865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 8.64554i | − | 0.517595i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.06746i | 0.182989i | 0.995806 | + | 0.0914946i | \(0.0291644\pi\) | ||||
−0.995806 | + | 0.0914946i | \(0.970836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.60619 | − | 6.60619i | 0.392697 | − | 0.392697i | −0.482951 | − | 0.875648i | \(-0.660435\pi\) |
0.875648 | + | 0.482951i | \(0.160435\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.7645 | + | 1.20925i | 0.756102 | + | 0.0716297i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.103570 | + | 0.103570i | 0.00611353 | + | 0.00611353i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.212901i | 0.0125236i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 18.2258i | − | 1.06842i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.3967 | + | 21.3967i | −1.25001 | + | 1.25001i | −0.294295 | + | 0.955715i | \(0.595085\pi\) |
−0.955715 | + | 0.294295i | \(0.904915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.99353 | − | 3.62007i | −0.174290 | − | 0.210769i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.0177703 | + | 0.0177703i | 0.00103114 | + | 0.00103114i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.2550 | − | 26.5917i | 0.708724 | − | 1.53784i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.1441 | 1.04581 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.1172 | + | 11.1172i | 0.638664 | + | 0.638664i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.85932 | − | 8.29497i | −0.392764 | − | 0.474969i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.43070 | − | 9.43070i | 0.538238 | − | 0.538238i | −0.384773 | − | 0.923011i | \(-0.625720\pi\) |
0.923011 | + | 0.384773i | \(0.125720\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.95273 | −0.224863 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0668 | −1.02448 | −0.512238 | − | 0.858844i | \(-0.671183\pi\) | ||||
−0.512238 | + | 0.858844i | \(0.671183\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.12544 | − | 1.12544i | 0.0636139 | − | 0.0636139i | −0.674584 | − | 0.738198i | \(-0.735677\pi\) |
0.738198 | + | 0.674584i | \(0.235677\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.497665 | + | 5.25321i | −0.0280403 | + | 0.295985i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.91087 | + | 8.91087i | −0.500484 | + | 0.500484i | −0.911588 | − | 0.411104i | \(-0.865143\pi\) |
0.411104 | + | 0.911588i | \(0.365143\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.181391 | 0.0101560 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.00405912i | 0.000226558i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.8217 | − | 16.8217i | −0.935985 | − | 0.935985i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.2547 | − | 17.1479i | 1.40088 | − | 0.951193i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.42001 | − | 3.42001i | −0.189127 | − | 0.189127i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.5768 | 0.803646 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0284 | 0.990929 | 0.495465 | − | 0.868628i | \(-0.334998\pi\) | ||||
0.495465 | + | 0.868628i | \(0.334998\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.47729 | − | 6.47729i | 0.354953 | − | 0.354953i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.465545 | − | 0.0441037i | −0.0254355 | − | 0.00240964i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.5933 | + | 22.5933i | 1.23074 | + | 1.23074i | 0.963681 | + | 0.267055i | \(0.0860505\pi\) |
0.267055 | + | 0.963681i | \(0.413950\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.35984 | 0.291106 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.217271i | 0.0117659i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.0688 | + | 14.0688i | −0.759641 | + | 0.759641i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.74753 | + | 10.3659i | 0.147922 | + | 0.558079i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.59353 | + | 3.59353i | −0.192911 | + | 0.192911i | −0.796953 | − | 0.604042i | \(-0.793556\pi\) |
0.604042 | + | 0.796953i | \(0.293556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.339995i | 0.0181995i | 0.999959 | + | 0.00909975i | \(0.00289658\pi\) | ||||
−0.999959 | + | 0.00909975i | \(0.997103\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.10524 | −0.325874 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6225 | + | 15.6225i | 0.831499 | + | 0.831499i | 0.987722 | − | 0.156223i | \(-0.0499317\pi\) |
−0.156223 | + | 0.987722i | \(0.549932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.68423 | − | 6.35428i | 0.407837 | − | 0.337250i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.92296 | − | 6.92296i | 0.366402 | − | 0.366402i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.3053 | 1.07168 | 0.535838 | − | 0.844321i | \(-0.319996\pi\) | ||||
0.535838 | + | 0.844321i | \(0.319996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.8788 | 0.730464 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.77773 | + | 7.77773i | 0.408225 | + | 0.408225i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.98268 | + | 0.472037i | 0.260806 | + | 0.0247075i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0788 | − | 11.0788i | −0.578307 | − | 0.578307i | 0.356130 | − | 0.934436i | \(-0.384096\pi\) |
−0.934436 | + | 0.356130i | \(0.884096\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.0620681i | − | 0.00323114i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.9422 | 1.60644 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.21203 | − | 4.21203i | 0.218091 | − | 0.218091i | −0.589603 | − | 0.807693i | \(-0.700716\pi\) |
0.807693 | + | 0.589603i | \(0.200716\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.12584 | + | 10.7345i | −0.161418 | + | 0.554326i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.1598 | + | 31.1598i | −1.60481 | + | 1.60481i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.3993 | 1.97244 | 0.986221 | − | 0.165435i | \(-0.0529029\pi\) | ||||
0.986221 | + | 0.165435i | \(0.0529029\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.11511 | −0.364518 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.00924 | − | 7.00924i | 0.358155 | − | 0.358155i | −0.504977 | − | 0.863133i | \(-0.668499\pi\) |
0.863133 | + | 0.504977i | \(0.168499\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0125068 | − | 0.132019i | 0.000637407 | − | 0.00672829i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.43676 | − | 5.43676i | −0.276366 | − | 0.276366i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.8149 | −1.20747 | −0.603733 | − | 0.797187i | \(-0.706321\pi\) | ||||
−0.603733 | + | 0.797187i | \(0.706321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.32793 | − | 18.0705i | 0.421161 | − | 0.913864i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.829140 | − | 0.829140i | −0.0418246 | − | 0.0418246i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.88850 | + | 8.17705i | −0.497544 | + | 0.411432i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.99927 | + | 3.99927i | −0.200718 | + | 0.200718i | −0.800308 | − | 0.599590i | \(-0.795330\pi\) |
0.599590 | + | 0.800308i | \(0.295330\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.5312i | 0.677409i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 17.2957i | − | 0.863704i | −0.901944 | − | 0.431852i | \(-0.857860\pi\) | ||
0.901944 | − | 0.431852i | \(-0.142140\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.3233 | − | 37.3233i | −1.85921 | − | 1.85921i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.72321 | − | 1.42497i | 0.0856272 | − | 0.0708073i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.162781 | + | 0.162781i | −0.00806876 | + | 0.00806876i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.5440i | − | 0.669708i | −0.942270 | − | 0.334854i | \(-0.891313\pi\) | ||
0.942270 | − | 0.334854i | \(-0.108687\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.7731i | 1.12332i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.50544 | − | 3.50544i | 0.172492 | − | 0.172492i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0544806 | + | 0.575082i | −0.00267435 | + | 0.0282296i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.2229 | + | 13.2229i | −0.647530 | + | 0.647530i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.4513 | 1.78076 | 0.890382 | − | 0.455215i | \(-0.150438\pi\) | ||||
0.890382 | + | 0.455215i | \(0.150438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 13.1308i | − | 0.639958i | −0.947425 | − | 0.319979i | \(-0.896324\pi\) | ||
0.947425 | − | 0.319979i | \(-0.103676\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.36786 | − | 4.36786i | −0.212372 | − | 0.212372i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.1619 | − | 11.6529i | 0.832476 | − | 0.565249i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.03231 | − | 8.03231i | 0.388711 | − | 0.388711i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.153431 | 0.00740772 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16.3040i | − | 0.785337i | −0.919680 | − | 0.392668i | \(-0.871552\pi\) | ||
0.919680 | − | 0.392668i | \(-0.128448\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.99454 | − | 6.99454i | 0.336136 | − | 0.336136i | −0.518775 | − | 0.854911i | \(-0.673612\pi\) |
0.854911 | + | 0.518775i | \(0.173612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.52217 | − | 16.0676i | 0.0729826 | − | 0.770383i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.52114 | + | 25.7985i | 0.455458 | + | 1.23411i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8220i | 1.18469i | 0.805684 | + | 0.592345i | \(0.201798\pi\) | ||||
−0.805684 | + | 0.592345i | \(0.798202\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.43123 | 0.0681538 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.6606 | − | 19.6606i | −0.934102 | − | 0.934102i | 0.0638575 | − | 0.997959i | \(-0.479660\pi\) |
−0.997959 | + | 0.0638575i | \(0.979660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.7310 | + | 14.6622i | −0.840532 | + | 0.695057i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.77247 | − | 2.77247i | −0.131133 | − | 0.131133i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.35828i | − | 0.252873i | −0.991975 | − | 0.126436i | \(-0.959646\pi\) | ||
0.991975 | − | 0.126436i | \(-0.0403540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.00155984i | 7.34498e-5i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.51294 | + | 4.51294i | 0.212036 | + | 0.212036i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.5299 | + | 24.8268i | 0.962459 | + | 1.16390i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.7631 | + | 11.7631i | 0.550255 | + | 0.550255i | 0.926514 | − | 0.376259i | \(-0.122790\pi\) |
−0.376259 | + | 0.926514i | \(0.622790\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.14884 | −0.193651 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.6561 | 1.33465 | 0.667325 | − | 0.744767i | \(-0.267439\pi\) | ||||
0.667325 | + | 0.744767i | \(0.267439\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.3062 | − | 22.3062i | −1.03666 | − | 1.03666i | −0.999302 | − | 0.0373556i | \(-0.988107\pi\) |
−0.0373556 | − | 0.999302i | \(-0.511893\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.2458 | + | 1.82326i | 0.892505 | + | 0.0845519i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.67121 | + | 8.67121i | 0.401256 | + | 0.401256i | 0.878675 | − | 0.477420i | \(-0.158428\pi\) |
−0.477420 | + | 0.878675i | \(0.658428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 0.493511i | − | 0.0227882i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.2274i | 0.655566i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.136631 | + | 0.136631i | 0.00628231 | + | 0.00628231i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.38382 | + | 28.1600i | −0.247027 | + | 1.29207i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.27165 | − | 9.27165i | −0.424520 | − | 0.424520i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.9417 | −0.682703 | −0.341352 | − | 0.939936i | \(-0.610885\pi\) | ||||
−0.341352 | + | 0.939936i | \(0.610885\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 55.9257i | − | 2.54999i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.6173 | + | 3.91841i | −0.483105 | + | 0.178294i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 40.5726 | + | 3.84366i | 1.84230 | + | 0.174532i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.71591 | − | 2.71591i | 0.123070 | − | 0.123070i | −0.642889 | − | 0.765959i | \(-0.722265\pi\) |
0.765959 | + | 0.642889i | \(0.222265\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 22.0017i | − | 0.994950i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.8186 | 0.488238 | 0.244119 | − | 0.969745i | \(-0.421501\pi\) | ||||
0.244119 | + | 0.969745i | \(0.421501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.1748 | + | 21.1748i | −0.953663 | + | 0.953663i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0433061 | + | 0.0358109i | −0.00194647 | + | 0.00160958i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.44091 | + | 7.44091i | 0.333770 | + | 0.333770i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.18810i | 0.366550i | 0.983062 | + | 0.183275i | \(0.0586698\pi\) | ||||
−0.983062 | + | 0.183275i | \(0.941330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7947 | 0.795008 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.69930 | + | 6.69930i | −0.298707 | + | 0.298707i | −0.840507 | − | 0.541800i | \(-0.817743\pi\) |
0.541800 | + | 0.840507i | \(0.317743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0924 | + | 22.4034i | −1.20560 | + | 0.996939i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.1643 | + | 17.1643i | −0.762293 | + | 0.762293i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 11.2505i | − | 0.498672i | −0.968417 | − | 0.249336i | \(-0.919788\pi\) | ||
0.968417 | − | 0.249336i | \(-0.0802123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.28200i | 0.233662i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.05455 | − | 4.05455i | 0.179013 | − | 0.179013i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.833593 | − | 8.79917i | 0.0367325 | − | 0.387738i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.109769 | + | 0.109769i | 0.00482762 | + | 0.00482762i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.74389i | − | 0.339919i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.5201i | 1.24949i | 0.780829 | + | 0.624745i | \(0.214797\pi\) | ||||
−0.780829 | + | 0.624745i | \(0.785203\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.3263 | + | 24.3263i | −1.06371 | + | 1.06371i | −0.0658877 | + | 0.997827i | \(0.520988\pi\) |
−0.997827 | + | 0.0658877i | \(0.979012\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.5892 | − | 2.21571i | −0.505795 | − | 0.0967013i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.3632 | − | 25.3632i | −1.10484 | − | 1.10484i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.4857 | + | 14.9416i | −0.760247 | + | 0.649634i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.10077 | −0.0911656 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.267952 | − | 0.267952i | −0.0116063 | − | 0.0116063i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.00903602 | 0.000856032i | −0.000390661 | 3.70095e-5i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.81830 | + | 3.81830i | −0.164772 | + | 0.164772i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.0359683 | −0.00154926 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2453 | 0.784426 | 0.392213 | − | 0.919874i | \(-0.371710\pi\) | ||||
0.392213 | + | 0.919874i | \(0.371710\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.72329 | − | 2.72329i | 0.116868 | − | 0.116868i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.33453 | − | 6.89203i | 0.357012 | − | 0.295222i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.56332 | − | 7.56332i | 0.323384 | − | 0.323384i | −0.526680 | − | 0.850064i | \(-0.676563\pi\) |
0.850064 | + | 0.526680i | \(0.176563\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.81366 | −0.205442 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 41.3870i | − | 1.76315i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.57538 | − | 9.57538i | −0.407187 | − | 0.407187i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.0531 | + | 15.7851i | 0.554074 | + | 0.670041i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.46308 | − | 8.46308i | −0.358592 | − | 0.358592i | 0.504702 | − | 0.863294i | \(-0.331602\pi\) |
−0.863294 | + | 0.504702i | \(0.831602\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.9416 | −1.98542 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.104265 | 0.00440206 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.86406 | − | 6.86406i | 0.289286 | − | 0.289286i | −0.547512 | − | 0.836798i | \(-0.684425\pi\) |
0.836798 | + | 0.547512i | \(0.184425\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.13034 | + | 11.9315i | −0.0475538 | + | 0.501964i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.66865 | + | 1.66865i | 0.0700766 | + | 0.0700766i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.0267 | −1.21686 | −0.608431 | − | 0.793607i | \(-0.708201\pi\) | ||||
−0.608431 | + | 0.793607i | \(0.708201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 34.8226i | − | 1.45728i | −0.684896 | − | 0.728641i | \(-0.740152\pi\) | ||
0.684896 | − | 0.728641i | \(-0.259848\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.78319 | + | 1.78319i | −0.0744939 | + | 0.0744939i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.6549 | + | 3.93022i | −0.986477 | + | 0.163901i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.76114 | + | 5.76114i | −0.239840 | + | 0.239840i | −0.816784 | − | 0.576944i | \(-0.804245\pi\) |
0.576944 | + | 0.816784i | \(0.304245\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 23.2541i | − | 0.966408i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.609627 | −0.0252916 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.233006 | + | 0.233006i | 0.00965013 | + | 0.00965013i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.28754 | − | 13.5909i | 0.0532332 | − | 0.561914i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.3927 | + | 27.3927i | −1.13062 | + | 1.13062i | −0.140542 | + | 0.990075i | \(0.544885\pi\) |
−0.990075 | + | 0.140542i | \(0.955115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.5736 | 2.04264 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.6398 | −0.643337 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.308745 | − | 0.308745i | −0.0126786 | − | 0.0126786i | 0.700739 | − | 0.713418i | \(-0.252854\pi\) |
−0.713418 | + | 0.700739i | \(0.752854\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.9512 | + | 16.8712i | 0.571944 | + | 0.691651i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.86990 | + | 8.86990i | 0.363021 | + | 0.363021i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.7873i | 1.42137i | 0.703510 | + | 0.710686i | \(0.251615\pi\) | ||||
−0.703510 | + | 0.710686i | \(0.748385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.9756 | −0.570076 | −0.285038 | − | 0.958516i | \(-0.592006\pi\) | ||||
−0.285038 | + | 0.958516i | \(0.592006\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.147877 | + | 0.147877i | −0.00602204 | + | 0.00602204i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.9543 | + | 15.6738i | −0.770600 | + | 0.637229i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.8569 | − | 10.8569i | 0.440667 | − | 0.440667i | −0.451569 | − | 0.892236i | \(-0.649136\pi\) |
0.892236 | + | 0.451569i | \(0.149136\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.0328 | 0.690204 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.7126 | −1.52569 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.7883 | + | 19.7883i | −0.799244 | + | 0.799244i | −0.982976 | − | 0.183733i | \(-0.941182\pi\) |
0.183733 | + | 0.982976i | \(0.441182\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.138170 | + | 0.0130896i | 0.00557155 | + | 0.000527823i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.8650 | − | 17.8650i | −0.719218 | − | 0.719218i | 0.249227 | − | 0.968445i | \(-0.419823\pi\) |
−0.968445 | + | 0.249227i | \(0.919823\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.9569 | −0.842330 | −0.421165 | − | 0.906984i | \(-0.638379\pi\) | ||||
−0.421165 | + | 0.906984i | \(0.638379\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.35555 | + | 2.00729i | 0.174782 | + | 0.0805497i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.1696 | − | 17.1696i | −0.687885 | − | 0.687885i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.2368 | − | 9.22225i | −0.929473 | − | 0.368890i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.101895 | + | 0.101895i | −0.00406930 | + | 0.00406930i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 38.0046i | − | 1.51534i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.1937i | 1.71952i | 0.510702 | + | 0.859758i | \(0.329386\pi\) | ||||
−0.510702 | + | 0.859758i | \(0.670614\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.31147 | + | 6.31147i | 0.250859 | + | 0.250859i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.50051 | − | 15.8389i | 0.0595459 | − | 0.628549i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.17870 | − | 6.17870i | 0.244809 | − | 0.244809i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4.45924i | − | 0.176405i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.13450i | 0.123805i | 0.998082 | + | 0.0619027i | \(0.0197169\pi\) | ||||
−0.998082 | + | 0.0619027i | \(0.980283\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.2196 | − | 24.2196i | 0.955128 | − | 0.955128i | −0.0439078 | − | 0.999036i | \(-0.513981\pi\) |
0.999036 | + | 0.0439078i | \(0.0139808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.2493 | − | 10.9562i | 0.521692 | − | 0.431400i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.2492 | − | 13.2492i | 0.520879 | − | 0.520879i | −0.396958 | − | 0.917837i | \(-0.629934\pi\) |
0.917837 | + | 0.396958i | \(0.129934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0527945 | 0.00207237 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.4020i | 0.799616i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.89395 | − | 3.89395i | −0.152382 | − | 0.152382i | 0.626799 | − | 0.779181i | \(-0.284365\pi\) |
−0.779181 | + | 0.626799i | \(0.784365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.02061 | − | 1.67089i | 0.0789517 | − | 0.0652872i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.58272 | − | 1.58272i | 0.0617477 | − | 0.0617477i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.97910 | −0.155004 | −0.0775019 | − | 0.996992i | \(-0.524694\pi\) | ||||
−0.0775019 | + | 0.996992i | \(0.524694\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 15.3507i | − | 0.597075i | −0.954398 | − | 0.298537i | \(-0.903501\pi\) | ||
0.954398 | − | 0.298537i | \(-0.0964988\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.9108 | + | 17.9108i | −0.695598 | + | 0.695598i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −30.1219 | − | 2.85361i | −1.16808 | − | 0.110658i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.4745 | − | 11.9850i | 1.25742 | − | 0.464060i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 11.4500i | − | 0.442682i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.120972 | 0.00467009 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.494649 | − | 0.494649i | −0.0190673 | − | 0.0190673i | 0.697509 | − | 0.716576i | \(-0.254292\pi\) |
−0.716576 | + | 0.697509i | \(0.754292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.80871 | + | 4.13656i | 0.108107 | + | 0.159216i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.8101 | − | 21.8101i | −0.838230 | − | 0.838230i | 0.150396 | − | 0.988626i | \(-0.451945\pi\) |
−0.988626 | + | 0.150396i | \(0.951945\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.0098i | 1.65056i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.1412i | 1.04005i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.1043 | + | 15.1043i | 0.577948 | + | 0.577948i | 0.934338 | − | 0.356389i | \(-0.115992\pi\) |
−0.356389 | + | 0.934338i | \(0.615992\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −50.6953 | − | 4.80264i | −1.93697 | − | 0.183500i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.5290 | + | 12.5290i | 0.478011 | + | 0.478011i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −80.0525 | −3.04976 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5555 | 1.08630 | 0.543151 | − | 0.839635i | \(-0.317231\pi\) | ||||
0.543151 | + | 0.839635i | \(0.317231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0419348 | − | 0.0419348i | −0.00159297 | − | 0.00159297i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.6470 | − | 32.2242i | −1.01078 | − | 1.22233i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.182088 | − | 0.182088i | −0.00689706 | − | 0.00689706i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 3.01089i | − | 0.113882i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.24702i | 0.198177i | 0.995079 | + | 0.0990887i | \(0.0315928\pi\) | ||||
−0.995079 | + | 0.0990887i | \(0.968407\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.1408 | + | 37.1408i | 1.40079 | + | 1.40079i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.6444 | − | 8.80215i | 0.400892 | − | 0.331508i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.2346 | − | 26.2346i | −0.986652 | − | 0.986652i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.96518 | −0.0738038 | −0.0369019 | − | 0.999319i | \(-0.511749\pi\) | ||||
−0.0369019 | + | 0.999319i | \(0.511749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.73841i | 0.215207i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.3556 | + | 38.8981i | 0.537623 | + | 1.45674i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0323572 | + | 0.341553i | −0.00121009 | + | 0.0127734i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.3410 | + | 17.3410i | −0.647613 | + | 0.647613i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.7947i | 1.14845i | 0.818698 | + | 0.574224i | \(0.194696\pi\) | ||||
−0.818698 | + | 0.574224i | \(0.805304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.32774 | 0.347383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.2090 | + | 13.2090i | −0.491249 | + | 0.491249i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35.4471 | + | 6.77702i | 1.31647 | + | 0.251692i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.78767 | + | 5.78767i | 0.214653 | + | 0.214653i | 0.806241 | − | 0.591588i | \(-0.201499\pi\) |
−0.591588 | + | 0.806241i | \(0.701499\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.8993 | −1.17984 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.2686 | − | 23.2686i | 0.859445 | − | 0.859445i | −0.131828 | − | 0.991273i | \(-0.542085\pi\) |
0.991273 | + | 0.131828i | \(0.0420845\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.301833 | + | 3.18606i | −0.0111333 | + | 0.117520i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.00371631 | − | 0.00371631i | 0.000136892 | − | 0.000136892i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.1921i | 1.40492i | 0.711725 | + | 0.702459i | \(0.247914\pi\) | ||||
−0.711725 | + | 0.702459i | \(0.752086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 35.0075i | − | 1.28603i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.32639 | − | 6.32639i | 0.232093 | − | 0.232093i | −0.581473 | − | 0.813566i | \(-0.697523\pi\) |
0.813566 | + | 0.581473i | \(0.197523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.75649 | − | 5.58711i | 0.247539 | − | 0.204696i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.182671 | + | 0.182671i | 0.00668358 | + | 0.00668358i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 0.00957882i | − | 0.000350002i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.1418i | 1.57427i | 0.616783 | + | 0.787134i | \(0.288436\pi\) | ||||
−0.616783 | + | 0.787134i | \(0.711564\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.85182 | − | 1.85182i | 0.0674842 | − | 0.0674842i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.9980 | + | 9.09452i | −0.400258 | + | 0.330984i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.0750 | − | 24.0750i | −0.875021 | − | 0.875021i | 0.117993 | − | 0.993014i | \(-0.462354\pi\) |
−0.993014 | + | 0.117993i | \(0.962354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.109459 | − | 0.0504453i | −0.00397312 | − | 0.00183105i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.3892 | −1.39161 | −0.695804 | − | 0.718232i | \(-0.744952\pi\) | ||||
−0.695804 | + | 0.718232i | \(0.744952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.07061 | + | 8.07061i | 0.292176 | + | 0.292176i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.874953 | − | 9.23574i | 0.0316340 | − | 0.333919i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.06914 | + | 9.06914i | −0.327468 | + | 0.327468i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.0561 | 0.903547 | 0.451773 | − | 0.892133i | \(-0.350792\pi\) | ||||
0.451773 | + | 0.892133i | \(0.350792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.5969 | 1.06591 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.8282 | + | 30.8282i | −1.10881 | + | 1.10881i | −0.115505 | + | 0.993307i | \(0.536849\pi\) |
−0.993307 | + | 0.115505i | \(0.963151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.11754 | + | 42.4587i | −0.291591 | + | 1.52516i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.2853 | + | 15.2853i | −0.548356 | + | 0.548356i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.355899 | 0.0127514 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.112065i | 0.00401002i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.10377 | − | 5.10377i | −0.182394 | − | 0.182394i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31.6717 | − | 3.00044i | −1.13041 | − | 0.107090i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.15839 | − | 9.15839i | −0.326461 | − | 0.326461i | 0.524778 | − | 0.851239i | \(-0.324148\pi\) |
−0.851239 | + | 0.524778i | \(0.824148\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.41395 | −0.263944 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.6483 | −0.449721 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.7809 | + | 20.7809i | −0.737950 | + | 0.737950i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.5949 | − | 18.6843i | 0.801360 | − | 0.662665i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.74270 | + | 5.74270i | 0.203417 | + | 0.203417i | 0.801462 | − | 0.598045i | \(-0.204056\pi\) |
−0.598045 | + | 0.801462i | \(0.704056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.6277 | −0.906644 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.2895i | 0.363562i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.0397753 | + | 0.0397753i | −0.00140364 | + | 0.00140364i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.48369 | − | 24.4616i | −0.228520 | − | 0.862158i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.6458 | − | 11.6458i | 0.409953 | − | 0.409953i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.6204i | 1.35782i | 0.734222 | + | 0.678910i | \(0.237547\pi\) | ||||
−0.734222 | + | 0.678910i | \(0.762453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.5982 | 1.46071 | 0.730356 | − | 0.683067i | \(-0.239354\pi\) | ||||
0.730356 | + | 0.683067i | \(0.239354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.8511 | − | 11.8511i | −0.415637 | − | 0.415637i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.9779 | + | 4.63995i | 1.71562 | + | 0.162530i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.1744 | − | 31.1744i | 1.09065 | − | 1.09065i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.4073 | 0.503432 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.2961 | 0.673440 | 0.336720 | − | 0.941605i | \(-0.390682\pi\) | ||||
0.336720 | + | 0.941605i | \(0.390682\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.457979 | − | 0.457979i | −0.0159642 | − | 0.0159642i | 0.699080 | − | 0.715044i | \(-0.253593\pi\) |
−0.715044 | + | 0.699080i | \(0.753593\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0705859 | − | 0.103956i | −0.00245749 | − | 0.00361928i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.39649 | + | 7.39649i | 0.257201 | + | 0.257201i | 0.823915 | − | 0.566714i | \(-0.191785\pi\) |
−0.566714 | + | 0.823915i | \(0.691785\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.0850i | 1.21855i | 0.792958 | + | 0.609276i | \(0.208540\pi\) | ||||
−0.792958 | + | 0.609276i | \(0.791460\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.0452 | −0.730050 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.19876 | − | 4.19876i | 0.145479 | − | 0.145479i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.75273 | + | 39.6127i | −0.129869 | + | 1.37086i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.11332 | − | 6.11332i | 0.211307 | − | 0.211307i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.1734 | −0.420274 | −0.210137 | − | 0.977672i | \(-0.567391\pi\) | ||||
−0.210137 | + | 0.977672i | \(0.567391\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0970 | −0.796448 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.16902 | + | 2.16902i | −0.0747050 | + | 0.0747050i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.5897 | − | 41.8292i | −1.18992 | − | 1.43897i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3541 | − | 18.3541i | −0.630653 | − | 0.630653i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.34256 | 0.320636 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.3873 | + | 39.8980i | −0.630309 | + | 1.36769i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.7887 | + | 28.7887i | 0.985708 | + | 0.985708i | 0.999899 | − | 0.0141916i | \(-0.00451747\pi\) |
−0.0141916 | + | 0.999899i | \(0.504517\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.17078 | + | 9.88091i | 0.279435 | + | 0.337920i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.7818 | + | 31.7818i | −1.08564 | + | 1.08564i | −0.0896730 | + | 0.995971i | \(0.528582\pi\) |
−0.995971 | + | 0.0896730i | \(0.971418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 14.5207i | − | 0.495441i | −0.968832 | − | 0.247721i | \(-0.920319\pi\) | ||
0.968832 | − | 0.247721i | \(-0.0796815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.146470i | 0.00499168i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.7792 | + | 34.7792i | 1.18390 | + | 1.18390i | 0.978726 | + | 0.205170i | \(0.0657748\pi\) |
0.205170 | + | 0.978726i | \(0.434225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.2387 | + | 1.63311i | 0.586132 | + | 0.0555275i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.150544 | + | 0.150544i | −0.00511273 | + | 0.00511273i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 0.144212i | − | 0.00489206i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.27679i | 0.0432624i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.8876 | − | 12.8876i | 0.436180 | − | 0.436180i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.37644 | − | 25.3315i | 0.249369 | − | 0.856361i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.7322 | + | 33.7322i | −1.13906 | + | 1.13906i | −0.150435 | + | 0.988620i | \(0.548067\pi\) |
−0.988620 | + | 0.150435i | \(0.951933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.2595 | −1.02063 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 42.1641i | − | 1.42054i | −0.703927 | − | 0.710272i | \(-0.748572\pi\) | ||
0.703927 | − | 0.710272i | \(-0.251428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.2200 | − | 13.2200i | −0.444887 | − | 0.444887i | 0.448763 | − | 0.893651i | \(-0.351865\pi\) |
−0.893651 | + | 0.448763i | \(0.851865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.443033 | − | 4.67652i | 0.0148924 | − | 0.157200i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.1329 | + | 18.1329i | −0.608845 | + | 0.608845i | −0.942644 | − | 0.333799i | \(-0.891669\pi\) |
0.333799 | + | 0.942644i | \(0.391669\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.7904 | 0.563132 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0251310i | 0.000841921i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.0453 | − | 25.0453i | 0.838109 | − | 0.838109i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.69468 | − | 9.30517i | −0.257205 | − | 0.311038i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.4687 | − | 10.1376i | 0.917154 | − | 0.338483i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 62.4020i | − | 2.08122i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.4000 | −1.81233 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.8298 | + | 12.8298i | 0.426949 | + | 0.426949i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.48800 | + | 6.63663i | 0.182427 | + | 0.220609i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.94315 | − | 7.94315i | −0.263748 | − | 0.263748i | 0.562827 | − | 0.826575i | \(-0.309714\pi\) |
−0.826575 | + | 0.562827i | \(0.809714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.7220i | 0.521467i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.75307i | 0.223739i | 0.993723 | + | 0.111870i | \(0.0356839\pi\) | ||||
−0.993723 | + | 0.111870i | \(0.964316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.00459071 | − | 0.00459071i | −0.000151930 | − | 0.000151930i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.01516 | − | 10.7157i | 0.0335601 | − | 0.354250i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.95663 | + | 1.95663i | 0.0646135 | + | 0.0646135i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.5597 | 0.843138 | 0.421569 | − | 0.906796i | \(-0.361480\pi\) | ||||
0.421569 | + | 0.906796i | \(0.361480\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.3370 | 0.439470 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.2508 | − | 19.2508i | −0.633648 | − | 0.633648i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.8920 | + | 25.7286i | −1.24588 | + | 0.845951i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.79500 | − | 2.79500i | −0.0917998 | − | 0.0917998i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.2581i | 0.434985i | 0.976062 | + | 0.217492i | \(0.0697877\pi\) | ||||
−0.976062 | + | 0.217492i | \(0.930212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.20668i | 0.268963i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.7752 | − | 12.7752i | −0.418240 | − | 0.418240i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0219885 | + | 0.232104i | −0.000719100 | + | 0.00759061i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.7271 | + | 10.7271i | 0.350441 | + | 0.350441i | 0.860273 | − | 0.509833i | \(-0.170293\pi\) |
−0.509833 | + | 0.860273i | \(0.670293\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.59162 | 0.0519405 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 45.1199i | − | 1.47087i | −0.677597 | − | 0.735434i | \(-0.736979\pi\) | ||
0.677597 | − | 0.735434i | \(-0.263021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.103062 | + | 0.279257i | 0.00335617 | + | 0.00909386i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.06648 | + | 3.36268i | −0.132283 | + | 0.109388i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.0586 | − | 19.0586i | 0.619320 | − | 0.619320i | −0.326037 | − | 0.945357i | \(-0.605713\pi\) |
0.945357 | + | 0.326037i | \(0.105713\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 13.6654i | − | 0.443597i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.6019 | −0.408644 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.48535 | + | 8.48535i | −0.274868 | + | 0.274868i | −0.831056 | − | 0.556189i | \(-0.812263\pi\) |
0.556189 | + | 0.831056i | \(0.312263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.59350 | − | 4.34562i | −0.116283 | − | 0.140621i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.128263 | + | 0.128263i | 0.00414616 | + | 0.00414616i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 53.7406i | − | 1.73537i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.7453 | 1.41114 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.00287023 | + | 0.00287023i | −9.24920e−5 | + | 9.24920e-5i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 51.7660 | + | 4.90408i | 1.66641 | + | 0.157868i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.8055 | − | 35.8055i | 1.15143 | − | 1.15143i | 0.165160 | − | 0.986267i | \(-0.447186\pi\) |
0.986267 | − | 0.165160i | \(-0.0528140\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 23.7895i | − | 0.764229i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 58.3681i | − | 1.87312i | −0.350506 | − | 0.936561i | \(-0.613990\pi\) | ||
0.350506 | − | 0.936561i | \(-0.386010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.2038 | − | 31.2038i | 1.00035 | − | 1.00035i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29.9831 | + | 5.73238i | 0.960229 | + | 0.183583i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.7797 | − | 40.7797i | −1.30466 | − | 1.30466i | −0.925216 | − | 0.379441i | \(-0.876116\pi\) |
−0.379441 | − | 0.925216i | \(-0.623884\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 0.258586i | − | 0.00826445i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4.83662i | − | 0.154421i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.9294 | − | 25.9294i | 0.827019 | − | 0.827019i | −0.160085 | − | 0.987103i | \(-0.551177\pi\) |
0.987103 | + | 0.160085i | \(0.0511767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.29830 | − | 34.8159i | 0.105092 | − | 1.10933i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.3074 | + | 10.3074i | 0.328087 | + | 0.328087i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.4886 | + | 15.4335i | 1.06488 | + | 0.490757i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.6862 | 0.688885 | 0.344443 | − | 0.938807i | \(-0.388068\pi\) | ||||
0.344443 | + | 0.938807i | \(0.388068\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.7480 | + | 12.7480i | 0.404545 | + | 0.404545i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.6159 | + | 17.8747i | −0.685269 | + | 0.566666i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.7469 | − | 20.7469i | 0.657059 | − | 0.657059i | −0.297624 | − | 0.954683i | \(-0.596194\pi\) |
0.954683 | + | 0.297624i | \(0.0961941\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.16028 | 0.289818 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1380.2.t.a.1333.23 | yes | 48 | |
5.2 | odd | 4 | inner | 1380.2.t.a.1057.24 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.t.a.1333.24 | yes | 48 | |
115.22 | even | 4 | inner | 1380.2.t.a.1057.23 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.t.a.1057.23 | ✓ | 48 | 115.22 | even | 4 | inner | |
1380.2.t.a.1057.24 | yes | 48 | 5.2 | odd | 4 | inner | |
1380.2.t.a.1333.23 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.t.a.1333.24 | yes | 48 | 23.22 | odd | 2 | inner |